| 李秀丽.强正则 $(\alpha,\beta)$-族和平移强正则 $(\alpha,\beta)$-几何[J].数学研究及应用,2008,28(4):928~934 |
| 强正则 $(\alpha,\beta)$-族和平移强正则 $(\alpha,\beta)$-几何 |
| Strongly Regular $(\alpha,\beta)$-Families and Translation Strongly Regular $(\alpha,\beta)$-Geometries |
| 投稿时间：2006-06-22 修订日期：2008-04-18 |
| DOI：10.3770/j.issn:1000-341X.2008.04.024 |
| 中文关键词: 射影空间 强正则$(\alpha,\beta)-$线汇 强正则$(\alpha,\beta)-$族 强正则 $(\alpha,\beta)-$几何. |
| 英文关键词:projective space strongly regular $(\alpha,\beta)$-regulus strongly regular $(\alpha,\beta)$-geometry. |
| 基金项目:青岛科技大学科研启动基金(No.0022327). |
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| 中文摘要: |
| 本文给出了强正则$(\alpha,\beta)-$族的概念,它是[4]和[5]中$SPG-$族概念的推广.进一步,给出了一种用强正则 $(\alpha,\beta)-$族构造强正则$(\alpha,\beta)-$几何的方法.另外,本文还证明了由强正则$(\alpha,\beta)-$线汇构造的强正则$(\alpha,\beta)-$几何是平移强正则$(\alpha,\beta)-$几何;当$t-r>\beta$时,反之亦成立. |
| 英文摘要: |
| In this paper, we introduce the concept of a strongly regular $(\alpha,\beta)$-family. It generalizes the concept of an SPG-family in [4] and [5]. We provide a method of constructing strongly regular $(\alpha,\beta)$-geometries from strongly regular $(\alpha,\beta)$-families. Furthermore, we prove that each strongly regular $(\alpha,\beta)$-geometry constructed from a strongly regular $(\alpha,\beta)$-regulus translation is isomorphic to a translation strongly regular $(\alpha,\beta)$-geometry; while $t-r>\beta$, the converse is also true. |
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